EXCHANGE UNIVERSITY OF PENNSYLVANIA ION ACTIVITY IN HOMOGENEOUS CATALYSIS THE VELOCITY OF HYDROLYSIS OF ETHYL ACETATE BY ROBERT PFANSTIEL A THESIS PRESENTED TO THE FACULTY OF THE GRADUATE SCHOOL IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN CHEMISTRY t?r (gollrgiatp ilrpsja GEORGE BANTA PUBLISHING COMPANY MENASHA, WIS. 1922 UNIVERSITY OF PENNSYLVANIA ION ACTIVITY IN HOMOGENEOUS CATALYSIS THE VELOCITY OF HYDROLYSIS OF ETHYL ACETATE BY ROBERT PFANSTIEL \\ A THESIS PRESENTED TO THE FACULTY OF THE GRADUATE SCHOOL IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN CHEMISTRY QHf* OJoUrgiatr fln-su GEORGE BANTA PUBLISHING COMPANY MENASHA, WIS. 1922 ACKNOWLEDGMENT This work was undertaken at the suggestion of Dr. Herbert S. Harned to whom the author is deeply indebted for its success. ION ACTIVITY IN HOMOGENEOUS CATALYSIS THE VELOCITY OF HYDROLYSIS OF ETHYL ACETATE As a result of considerable evidence, Mac Innes (Jour. Amer. Chem. Soc. 41, 1086 [1919]) has arrived at the conclusion that in solutions of the same molality of hydrochloric acid, lithium, sodium, and potassium chlorides, the chlorine ion has the same activity. He further made the assumption that in a solution of a given strength, the activities of the potassium and chlorine ions are the same. These hypotheses received considerable confirmation in dilute solu- tions from the electromotive force measurements of Ming Chow (Jour. Amer. Chem. Soc. 42, 477 [1920]) and in concentrated solu- tions by Harned (Jour. Amer. Chem. Soc. 42, 1808 [1920]). On the basis of these assumptions, Harned calculated from existing electro- motive force data the individual ion activity coefficients of these uni-univalent electrolytes. If Mac Innes' assumptions are correct it follows from these calculations that the activity coefficient of the hydrogen ion in dilute solutions of hydrochloric acid decreases until a concentration of 0.15 M. is reached and then increases quite rapidly. In any event, this activity coefficient must exhibit a minimum in the neighborhood of from 0.1 M. to 0.2 M. concentra- tion. These conclusions, if true, or valid within narrow limits, will be of considerable importance in the calculation of equilibria in solutions as well as homogeneous catalysis. Consequently, this investigation was undertaken with the purpose of finding out whe- ther further support for the above hypothesis could be obtained from a study of hydrogen ion catalysis. It has been found that the monomolecular velocity constant of hydrolysis of ethyl acetate in dilute solutions of hydrochloric acid is roughly proportional to the concentration of the acid. It was first thought that the velocity of hydrolysis was proportional to the hydrogen ion concentration, but it was soon found that the velocity constant increased with increasing acid concentration more rapidly than the hydrogen ion concentrations as computed from the con- ductance or conductance viscosity ratios. To explain this, Senter 1 2 ION ACTIVITY IN HOMOGENEOUS CATALYSIS (Trans. Chem. Soc., 91, 467 [1907]), Acree (Amer. Chem. Jour., 37, 410, and 38, 258 [1907]), Taylor (Meddel. K. Vetensk. Nobelinst., 2, No. 37 [1913]), and others have proposed the theory that the undissociated acid molecule, as well as the hydrogen ion, exerts a catalytic effect. In contradistinction to this, another theory has been proposed which relates the reaction velocity to the ion ac- tivities as defined by G. N. Lewis (Proc. Amer. Acad. Arts Sci. 43, 259 [1907]; Jour. Amer. Chem. Soc., 35, 1 [1913], etc.). Lewis has shown that in a chemical equilibrium the exact thermodynamic expression for the law of mass action of a general reaction such as aA+bB+ . . . .=>dD+eE+ .... is * = - ............... ..... .............. (1) ttj 4 where a^ a B) etc., represent the activities of the species A, B, etc., respectively, and K is an equilibrium constant. Thus, if the equili- brium is a dynamic one, the velocity from left to right and the velocity from right to left will be given respectively by If the velocities depend on successive states of equilibria, and no interfering factors such as contact surfaces, light radiation, etc., are present, the above equations for the velocities are a thermo- dynamic necessity. At the present time the mechanism of ester hydrolysis is not well known. The theory which has the most evidence in its favor is the one which assumes the formation of an intermediate compound (Stieglitz Congress of Arts and Sciences St. Louis 4, 276 [1904]). Here the reaction takes place in two steps. The first is a rapid reac- tion between the ester, hydrogen ion, and water, to form the inter- mediate compound, and the second is a slow decomposition of the intermediate compound producing the alcohol and acid, and regen- erating the hydrogen ion. Thus [-0-H -| + Vro-n CH 3 C O C 2 #5j ........ (a) ^ [-0-H -I + Vro-n CH 3 C C 2 H<,]=?CH 3 COOH+C 2 H b OH+H + ....... (b) ION ACTIVITY IN HOMOGENEOUS CATALYSIS The equilibrium of reaction (a) is represented by a e o H a w where 0;, a e , a E , and a w are the activities of the intermediate com- pound, ester, hydrogen ion, and water species. The velocity of the reaction from left to right will be given by i = ka\ Hence DI = ki a e - H a w (3) Throughout this paper ki will represent the velocity from left to right. Since by definition F e -c equals a e , where F e is the activity co- efficient of the ester and c is its concentration, substitution in (3) gives Vi = ki(F e 'c)-a E -a w (4) At a given temperature ki remains constant under changing conditions of all other factors in equation (4) Let k\=ki #H ' #wj Then ^ =ki (4a) #H * a w Substituting the value of k\, in (4) gives 0i = *Y(F e -c) (4b) From (4a), k\ is proportional to #H and a w . During the course of reaction in a given experiment #H an d a w remain constant and k\ therefore represents the velocity constant in each experiment. Since the velocity constant is obtained by measurement of c, equa- tion (4b) shows that k\F 6 instead of k\ is obtained. Therefore in the Tables to follow k'iF e will always represent the velocity constant. k'iF Equation (4a) shows that will not remain constant if F e vary. #H * a w F e will vary if the solubility of the ester changes with changing hydrochloric acid concentration because F e is a function of the solubility. This can be seen from the following thermodynamic reasoning: The activity of the ester in a saturated solution in the presence of the liquid ester at the same pressure and temperature will always have the same value. Therefore, if a', a", a'", etc., represent the activities of the ester in varying acid concentrations, and C', C", C"' etc., represent the concentrations of the ester in the saturated solutions, Thena'"-a'"=etc. ION ACTIVITY IN HOMOGENEOUS CATALYSIS C or " '" Substituting 6", 5", 5'", etc., or the solubilities for the conten- trations in the saturated solutions gives F e 'S' = F e "S" = F e '"S f " = F e S = constant ............ (5) From (4a) and (5) is obtained kl/ Fe - S = h \F 9 S) = constant ................... (Sa) flH'tfw Earlier work on this subject is not sufficient to prove the validity of equation (5a). A compilation of previous data taken from the work of Taylor (Meddel. K. Vetensk. Nobelinst., 2, No. 37, [1913]), Kay (Proc. Royal Soc. Edinb., 22, 484 [1897]) and Lunden (Zeit. Phy. Chem., 49, 189 [1904]) on the hydrolysis of ethyl acetate and other esters is contained in a paper by Schreiner (Zeit. anorg. chem., 116, 102, [1921]). These results are reproduced in Table I. TABLE I Ethyl Acetate Hydrolysis Hydrochloric acid Concentration (k\ F e ) 10 6 (feV-flJ-lO 8 c c 0.010 2.93 293. 0.025 6.99 280. 0.050 13.83 278. 0.100 28.29 283. 0.132 38.10 288. 0.150 43.20 288. 0.200 57.00 285. 0.250 71.60 286. 0.479 138.00 288. 0.493 145.00 296. * Thus, the velocity constant divided by the concentration passes through a minimum at about 0.05 M. hydrochloric acid. This is similar to the behavior of the activity coefficient of the hydrogen ion as mentioned above. This evidence is by no means conclusive, but is suggestive due to the parallelism between these properties. Consequently, further careful work has been undertaken in order to clear up, if possible, some of the difficulties. I. EXPERIMENTAL The experimental method employed throughout in determining the velocity constants is the same as that usually employed, namely, I ION ACTIVITY IN HOMOGENEOUS CATALYSIS 5 titration from time to time of' the total acid present in the ester- hydrochloric acid mixture by means of sodium and barium hydroxide solutions. Densities of all the solutions were determined so that the calculations could be made on either a weight or a volume normal basis. Further, all solutions were so standardized that it was possible to compute the absolute quantities of all the molecular species pres- ent at any time during the course of the reaction. Since calcula- tions were made by both the monomolecular formula and by the general kinetic formula for the reaction, it will be necessary to discuss the procedure in some detail. (a) MATERIALS Ethyl acetate was prepared from alcohol and acetic acid, and purified in the usual way. After repeated fractional distillation, the portion which passed over between 77 and 78 was collected for the investigation. Analysis of this fraction gave 98.81% saponifiable ester, free from acetic acid. Tests for free acetic acid were made from time to time during the course of the investigation and in no case was it found present. Constant boiling hydrochloric acid was diluted to 3M, and checked by gravimetric analysis. All solutions of the acid were made from this sample by the weight method and were correct to within 0.1% of the total hydrochloric acid content. Conductivity water freed from carbon dioxide by boiling was employed. The sodium hydroxide and barium hydroxide solutions used to titrate the total acid (hydrochloric, and acetic formed during the hydrolysis of the ester) were kept in carbon dioxide free bottles. The sodium hydroxide solutions were freed from carbonate by the addition of small quantities of barium hydroxide. All flasks used were cleaned with a sulphuric-chromic acid mix- ture, followed by the introduction of a jet of steam. After drying, they were provided with paraffined cork stoppers. (b) METHOD OF PROCEDURE Each determination was carried out in a % liter flask. In all the determinations 200 grams of water were employed. The molal concentration of the hydrochloric acid (mols of hydrochloric acid in 1000 grams of water) varied from 0.01 to 1.5. In a given series the same quantity of ethyl acetate was added to each flask. Thus in every determination of a given series the same quantity of water and the 6 ION ACTIVITY IN HOMOGENEOUS CATALYSIS same quantity of ester was employed, the only variable being the hydrochloric acid content. Two series of results were obtained using 5 c.c. and 1 c.c. of ester to 100 grams of water. In every determination, the quantity of hydrochloric acid solu- tion necessary for a given molal concentration of hydrochloric acid in 200 grams of water was calculated, and then weighed in a small weighing bottle, care being taken to avoid loss by evaporation while weighing. It was then washed into a previously weighed 250 c.c. flask. Water was then added until the weight obtained was equal to the weight of the flask, the HC1, and 200 grams of water. The flask was then placed in a thermostat in which a temperature of 25 0.01 was maintained. After the contents of the flask had acquired the same temperature as the bath, ethyl acetate at 25 was added to the solution from a pipette. Two series of experiments were conducted, differing from one another only in the ester concen- tration. In the one series 10 c.c., and in the other 2 c.c. of ethyl acetate were added to each solution. In each case, the quantity of ester added was determined by taking the average weight of several pipetted portions of ethyl acetate, the same conditions as to tem- perature and delivery of pipette being observed. The addition of as much as 10 c.c. of ester caused a noticeable rise in temperature, amounting to 1 in cases where the molal concentration of hydrochloric acid was 0.5 or higher. Therefore before pipetting for the initial titration, it was necessary to wait until the temperature was reduced to 25. As soon as all the ester was dissolved and the liquid had assumed the temperature of the bath, a 10 c.c. portion was withdrawn with a pipette and delivered into a beaker containing a little water and some phenolphthalein. While the pipette was delivering, sodium hydroxide from a burette was introduced at a rate sufficient to neutralize the hydrochloric acid in the hydrolyzing solution as fast as it was discharged from the pipette. Since the time of the initial titration and all subsequent titrations were noted the time always taken was the instant when the pipette was half discharged. From eight to ten titrations were made in each determination at successive time intervals during the course of the reaction. A 0.04426 N. barium hydroxide solution was employed in all cases as titrating agent, and for solutions containing the higher hydrochloric acid concentrations a stronger solution of sodium hydroxide was also used. In the latter case, the initial titrations were made with the stronger alkali, and ION ACTIVITY IN HOMOGENEOUS CATALYSIS 7 the subsequent titrations were 'made by first adding the same amount of sodium hydroxide as was used in the initial titration and then completing the determination by the addition of barium hydroxide. (c) KINETICS OF THE REACTION In what follows, a very careful study has been made of the velocity constants calculated by both the simplified and approxi- mate monomolecular reaction equation, and the more general kinetic equation which takes into consideration the reverse reaction. (1) The Kinetics of the First Order Reaction. The general equation for the kinetics of the reaction, RCOOR'-}- H^O^RCOOH-\-R'OH t in going from left to right and assuming that the activities of the four molecular species are proportional to their concentrations and that the hydrogen ion activity remains constant, will be dr =%" (A-x) (B-x)-k z x* ............... (6) at dx where is the velocity, A and B the initial concentrations of ester dt and water, x the amount of ester changed in the time, t, and ki" and k% are the velocity constants of hydrolysis and esterification respec- tively. Since the water concentration, B, varies only slightly during the reaction, and since the reaction goes nearly to completion when a relatively large quantity of water is present, equation (6) may be reduced to the simpler and approximate monomolecular equation ^=k i "(A-X) .................... ' ....... (7) dt which upon integration takes the well known form t A X This equation when expressed in terms of the titers becomes kS'^ln 7 ^^ ........................ (9) t Toc-r where T> is a number slightly greaterf than the final titer, T the initial titer, and T the titer at any time /. k"-W*& t Explained later. 8 ION ACTIVITY IN HOMOGENEOUS CATALYSIS (2) The General Kinetic Equation. In equation (6), namely, = k l " (A-x) (B-x)-k 2 x 2 , V and k* dt are both unknowns. Therefore k z must be eliminated. Let ^ = = *i" (A-x) (B-x)-k z x 2 , dt kz (Ax) (B x) r , f .... . . x then = = K (equilibrium constant) ki" x 2 and k* = ki"-K (10) K can be determined experimentally since = represents the dt end point in a titration. (Subst. for k* in [6]) - = /' (A-x) (B-x)-^" Kx 2 (11) dt or = fc" {x*-(A+B)x+AB} -h" Kx* dt or = RI (I A dt ' \ 1-K 1-K dx =k 1 " (l-K)dt.. ..(12) . A+B .A-B x 2 x+ '1-K 1-K C.. ..(13) dx xZ _AB A^B 1-K 1-K To integrate the expression on the left hand side of equation (13), let and a* -4-f. ........................ (15) 1 K ION ACTIVITY IN HOMOGENEOUS CATALYSIS r dx _ = r dx Then / 2 __ J X l-K l-K /dx I dx I = J J = In (ft x)- In (a x) = ft a ft a 1 . ft x ,. = In (lo) a a Equation (13) becomes In^^=k 1 " (l-k)t+C ......... (17) ft a ax To evaluate the constant C, let t = o, then x = o, and ft- a a Subst. value of Cin (17): In a(/3 ~^ = ^"(l-ff)* ........ (18) 2.3026 atf-.) (1-X) (|8-o)< B (a-*) For substituting back in equation (19) the values of a and j3, in terms of A, B, and K, equations (14) and (15) must be solved simul- taneously. 4A-B (l-K) 2 (l-K) A+B-V(A+B)*-4 A-B (l-K) 2 (l-K) 2.3026 A+B-(A+B)*-4 AB(1~K) -4: A-B (l-K) A+B+(A +B)*-4 AB(l-K) -4 AB l-K-2 l-K)x -4: AB (l-K)-2 (l-K)x 10 ION ACTIVITY IN HOMOGENEOUS CATALYSIS Equation (20) is reduced to a simpler form by letting 2.3026 A+B-V(A+B) 2 -4A-B(1-K) V(A+B) 2 -4AB (1-K) A+B+V(A+B)*-4A'B(1-K) X 2 (l-K), and n = A+B- V(A+B)*-4: A-B (1-K). By substitution in (20) Griffith and W. C. McC. Lewis, (Jour. Chem. Soc., 109, 67 [1916]) indicate how equation (6) may be integrated by a different substitu- tion. Knoblauch (Zeit. fur Physk. Chemie 22, 268, [1897]) integrated a similar equation by a different substitution. (D) CALCULATION, AND TABLES OF VELOCITY CONSTANTS COMPUTED FROM MONOMOLECULAR EQUATION In computing ki" according to the monomolecular equation (9), Too represents the quantity of alkali which would be required for titration after complete hydrolysis. Since the reaction does not go to completion, T cannot be determined experimentally. There- fore r w was calculated in each experiment as follows: The weight of 10 c.c. of the solution, delivered from the pipette used in each titration, was determined. Let this be "a." In the preparation of the solutions the weight of each component was known. Let b equal the weight of the water, d the weight of hydrochloric acid, and e the weight of the ester in the reaction flask. Then - d is b+d+e the number of grams of hydrochloric acid, and - e is the number of grams of ethyl acetate (assuming no hydrolysis), in each pipette. Therefore, the alkali equivalent of both the hydrochloric acid and the ethyl acetate in cubic centimeters, or T M is readily obtained. It is important to note that employing this value for Too gave lower values for the velocity constants than would have been obtained by taking for T> the titration value at equilibrium. Al- though the velocity constants show a greater variation in value (due to the influence of the reverse raction) as the reaction approaches equilibrium, than is apparent when the final titration value for 7\o is taken for calculating the results, the values of the velocity constants ION ACTIVITY IN HOMOGENEOUS CATALYSIS 11 at the beginning of the reaction are more consistent. For the above reason the values for k\" will be lower than other values given in the literature. In Table II the results of an average experiment, calcu- lated by the above method, are compared with the results obtained by using the titer value for T M . Too = calculated value, and T'*> = titer value. TABLE II Temp. = 25c. 0.15 M. HC1 Too-r =97.52 r'oo- To =94.55 Time T^-T (V F.) - 10* T^-T (ki* F e ) 10 4 Minutes 157 84.52 9.112 81.55 9.402 281 75.49 9.112 72.52 9.440 421 66.27 9.176 63.30 9.526 526 60.39 9.110 57.42 9.480 736 49.92 9.098 46.95 9.502 1148 34.55 9.039 31.58 9.552 1455 26.57 8.934 23.60 9.536 1829 19.42 8.823 16.45 9.560 2091 15.77 8.713 12.80 9.562 2966 8.59 8.190 5.62 9.519 The velocity constants for the different acid concentrations are given in Table III. They are the mean of the constants for the first half of the reaction which in all cases gave concordant results. The constants for two series, differing in the concentration of the ester employed, are given. In each series two determinations of the velocity constants for each acid concentration were made and the mean value recorded. ki'F e is the mean velocity constant, Ci is the molal concentration of hydrochloric acid, and C% is the normal concentration of hydrochloric acid. (e) CALCULATIONS OF THE EQUILIBRIUM CONSTANT In the calculation of the velocity constant by the general equa- tion, it is necessary to employ a value for the equilibrium constant. The classic work of Berthelot and St. Gilles gives the value of 4. Knoblauch, (Zeit. physik. Chem., 22, 268 [1897]) using an equi- molecular mixture of alcohol and water, a high concentration of ester, and hydrochloric acid as a catalyst, obtained 2.67. Jones and 12 ION ACTIVITY IN HOMOGENEOUS CATALYSIS 0.01 0.03 0.05 0.07 0.10 0.15 0.20 0.30 0.50 0.70 1.00 1.50 0.01 0.03 0.05 0.07 0.10 0.15 0.20 0.30 C 2 0.00952 0.02857 0.04759 0.06666 0.09510 0.1425 0.1900 0.2840 0.4726 0.6604 0.9354 0.1391 0.00987 0.02961 0.0493 0.0690 0.0985 0.1477 0.1966 0.2944 TABLE III 0.470 N. Ester (fc'FeHO 6 (*i'F e )-10 Ci 6.11 611 18.30 610 30.00 600 41.79 597 60.15 601 91.10 607 122.2 611 185.5 618 312.4 625 45t).0 643 640.0 640 1006. 671 0.100 N . Ester 6.37 637 18.96 632 31.74 634 44.44 635 63.56 636 95.54 637 129.0 645 197.2 657 c, 642 641 630 627 632 639 643 653 661 681 684 723 645 640 644 644 645 647 656 670 Lapworth (Trans. Chem. Soc., 99, 1427 [1911]) found that in the presence of large quantities of hydrochloric acid the equilibrium con- stant was somewhat greater than 4. With methyl acetate, at a con- centration of 1.15 to 1.74 normal, Griffith and Lewis (Jour. Chem. Soc. 109, 67 [1916]) obtained for K, in the presence of N/2 hydro- chloric acid, 4 . 30, 4 . 52, 4 . 66, and 4 . 80. Since no definite information regarding the value of K for the hydrolysis of ethyl acetate in the presence of hydrochloric acid of concentrations here employed could be obtained, the equilibrium constant was determined at each acid concentration. Great accuracy could not be obtained on account of the experimental conditions. The large concentration of water forces the reaction to within 3% of completion, thus mag- nifying the errors of the determination. However, when the results in Table IV are compared with those of Griffith and Lewis who employed an ester concentration four times greater than that em- ployed in this investigation, the concordance of values must be considered excellent, and a good confirmation of the accuracy of this work. ION ACTIVITY IN HOMOGENEOUS CATALYSIS 13 K = TABLE IV (A-x)(B-x) Ci A X B K 0.01 0.4737 0.4600 52.85 3.39 0.03 0.4737 0.4582 52.85 3.87 0.05 0.4737 0.4596 52.85 3.50 0.07 0.4737 0.4581 52.85 3.89 0.10 0.4731 0.4576 52.79 3.87 0.15 0.4728 0.4583 52.74 3.61 0.20 0.4727 0.4567 52.73 4.01 0.30 0.4713 0.4554 52.63 4.00 0.50 0.4701 0.4545 52.45 3.93 0.70 0.4679 0.4533 52.20 3.68 1.00 0.4652 0.4519 51.91 3.35 Mean 3.74 Since there is no apparent increase or decrease of the equilibrium constant within the limits of these hydrochloric acid concentrations, and since the mean value checks, within the present experimental er- ror, the value of Berthelot and St. Gilles, the value of 4 for the equilibrium constant has been employed in all subsequent calcula- tions. (f) METHOD OF CALCULATION, AND TABLES OF VELOCITY CONSTANTS OF HYDROLYSIS COMPUTED FROM THE GENERAL EQUATION Substituting the value of 4 for K in equation (21), the final form for the general kinetic equation is ..(22) t n 6x In order to employ this equation it is necessary to obtain the values of A, the initial concentration of ester; B, the initial concentra- tion of water; and x, the concentration of the ester changed in a time t. A and B were readily obtained since the weight of the ester and water, and the density of the solutions were known. Their calculation needs no explanation. Therefore, it remains only to show how x is calculated and how a slight change is made in To and in the first reading of /. From equation (22) when t equals 0, x must equal zero. Under the experimental conditions, it is impossible to start the experiment at the beginning of the hydrolysis. When the first titra- 14 ION ACTIVITY IN HOMOGENEOUS CATALYSIS tion is made, some ester has hydrolyzed, and x therefore has an appreciable value when / equals 0. Therefore T Q , the initial titration, is corrected to a value which will give x equal 0, and / is corrected so as to make the beginning of the time the moment when x equals . The following consideration will explain how this correction is made: Let the initial titration be TQ. Calculate 7\o. Then the ester equiva- lent, T e , of the contents of one pipette of the solution in terms of cubic centimeters of alkali is calculated. Then T> - T e = T' Q . T' Q is less than T by a quantity of alkali equivalent to the acetic acid formed from the beginning of hydrolysis up to the time of the first titration. Now the lapse of time from the beginning of hydrolysis up to the time of the first titration may be computed from the equa- tion: (23) This time is added to the time period of each successive titration. rp